Post on 22-Jan-2018
Narrow banking with modern depository institutions:
Is there a reason to panic?
Hugo Rodríguez MendizábalInstituto de Análisis Económico (CSIC), MOVE, and
Barcelona GSE
EUI, March 17, 2017
• What would be the effects of narrow banking?
Question
(i.e. 100% reserve requirement)
“(...) 100% reserve banking is a dangerous proposal that would do substantial damage to the economy by reducing the overall amount of liquidity. Furthermore, the proposal is likely to be ineffective in increasing stability since it will be impossible to control the institutions that will enter in the vacuum left when banks can no longer create liquidity. Fortunately, the political realities make it unlikely that this radical and imprudent proposal will be adopted.”
Diamond and Dybvig, JofB 1986
• What would be the effects of narrow banking?
Question
(i.e. 100% reserve requirement)
“(...) 100% reserve banking is a dangerous proposal that would do substantial damage to the economy by reducing the overall amount of liquidity. Furthermore, the proposal is likely to be ineffective in increasing stability since it will be impossible to control the institutions that will enter in the vacuum left when banks can no longer create liquidity. Fortunately, the political realities make it unlikely that this radical and imprudent proposal will be adopted.”
Diamond and Dybvig, JofB 1986
A LBank
DepositLoan
The traditional model (D&D , JPE 1983)
Reserves
NB advocates: fractional banking → risk of bank runs
• suspension of convertibility
• deposit insurance
borrower saver
NB detractors: narrow banking → huge efficiency costs
→ separation of financial instit.
cheaper alternatives to avoid bank runs
Question
• What would be the effects of narrow banking?
(i.e. 100% reserve requirement)
This paper: including a realistic description of modern monetary systems radically changes the predictions of the traditional model (at least regarding narrow banking)
• What are the effects of narrow banking?
Answer
• reserves are not competing with bank loans
• reserves have indirect effect on bank intermediation through cost of producing loans and deposits
• if central banks remunerated required reserves at refinancing rate (Eurosystem), then narrow banking would have no effecton liquidity creation and bank intermediation
• no need to separate financial institutions
• collateral at central bank’s OMOs? seigniorage?
• …Switzerland and Iceland are seriously considering introducing narrow banking in their monetary systems
By the way…
• The model
• Liquidity risks
• Calibration
• Conclusions
• Solvency risks
Outline
• Literature review
• Static general equilibrium model
• Continuum of risk-averse agents (workers & entrep.)
• Commercial banks
• Government sector (central bank and deposit insurance)
• Continuum of risk-neutral investors
The model
Economy consists of a continuum of identical islands
The economy
1
Labor market(competitive)
locations
Entrepreneurs
Workers
The real side
d
~ X(x)x = fraction of loans repaid to bank
Friction 1: market segmentationin banking services
Banks
Banks
time
A LBank
Banks
time
A LBank
Loan entrep. dLdL
: loan and deposit creation
dL
Deposit workerDeposit entrep.
• Banks as creators of money
Literature review
Federal Reserve
Holmes (FRBB, 1969), Keister & McAndrews (FRBNY, 2009)
Bank of England
McLeay et al. (BofE, 20014a, 2104b), King (2012), Turner (2013)
Financial sector
BIS
Borio & Disyatat (BIS, 2009)
Standard & Poor’s (2013), Pinetree Capital Ltd. (2012)
Banks
time
A LBank
Loan entrep. dLdL
: net worth
dL
Deposit worker
Net worth
NW
(1 + il)dL – (1 + id)dL
Banks
time
A LBank
Loan entrep. dLdL
: solvency risks
dL
Deposit worker
Net worth
NW
(1 + il)dL – (1 + id)dL
Solvency risk x ~ X(x) x [0, 1]
x(1 + il)dL – (1 + id)dL
Assets dQ Equity dQ
IOU
dQ
Investor
Capital constraint dQ ≥ k dL
x (1 + il)dL + dQ – (1 + id)dLx
Banks
time
A LBank
Loan entrep. dLdL
: liquidity risks
dL
Deposit worker
Net worth
NW
Solvency risk x ~ X(x) x [0, 1]
Assets dQ Equity dQ
IOU
dQ
Investor
Capital constraint dQ ≥ k dL
x (1 + il)dL + dQ – (1 + id)dLx
d
1 - d
For bank …
deposit outflow(1 – d)dL
deposit inflow
d(1 – d)L
net deposit inflow
(1 – d)d(L – L)dL
^
^
Banks: liquidity risks
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dLDeposit entrep.dL
dQ
dL
OMO
M
Reserves M Loan from CB M
Net worth
x(1 + il)dL + dQ – (1 + id)dL – ioMx(1 + il)dL + dQ – (1 + id)dLx
NW
Banks: liquidity risks
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dLDeposit entrep.dL
dQ
dL
Flow of funds (deposits and reserves)
M
Reserves M Loan from CB M
FF = (1 – d)d(L – L)^
FF
Reserves M + FF
dL + FFDeposit worker
e ~ Y(0, se)
Net worth
x(1 + il)dL + dQ – (1 + id)dL – ioMx(1 + il)dL + dQ + FF – (1 + id)(dL + FF)– ioM
e
x
NW
Banks: liquidity risks
– edL
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dL
dQ
dL
Interbank market
M
Loan from CB M
FF
Reserves M + FF
I
Reserves M + FF – I
Loan interb. I
Net worth
x(1 + il)dL + dQ + FF – (1 + id)(dL + FF)– ioM
riskpremium
x
NW
e
dL + FFDeposit worker
+ i × I(I > 0) + (i + s)× I(I < 0)
Banks: liquidity risks
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dL
dQ
dL
M
Loan from CB M
FF
I
Reserves M + FF – I
Loan interb. I
x
NW
e
Net worth
x(1 + il)dL + dQ + FF – (1 + id)(dL + FF)– ioM
Remuneration of required reserves
dL + FFDeposit worker
+ i × I(I > 0) + (i + s)× I(I < 0) + ir rdL
reserve requir.
Banks: liquidity risks
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dL
dQ
dL
M
Loan from CB M
FF
I
Reserves M + FF – I
Loan interb. I
x
NW
e
Net worth
x(1 + il)dL + dQ + FF – (1 + id)(dL + FF)– ioM
dL + FFDeposit worker
+ i × I(I > 0) + (i + s)× I(I < 0) + ir rdL
Banks: role of cash?
So expost net worth is
e ~ Y(0, se)
LiIIsiIiIMiFFi od rd-- r)0()()0(
Reserve position
LLLLM rd-ed--d-d )ˆ)(1(
LLLFF ed--d-d )ˆ)(1(
> 0 excess reserves
LLLLM rd-ed--d-d )ˆ)(1( < 0 reserve deficit
LLLLMI rd-ed--d-d )ˆ)(1(
LiQLix dl d-dd )1()1(
Banks: liquidity risks
So expost net worth is
LiQLix dl d-dd )1()1(
e ~ Y(0, se)
LiIIsiIiIMiFFi od rd-- r)0()()0(
LLLFF ed--d-d )ˆ)(1(
LLLLMI rd-ed--d-d )ˆ)(1(
I >< 0 e <
> er-d
-d-d
L
LLM )ˆ)(1(
LiIdsiIdiMiFFiL od
MrdeYeY-- r
e
e
-
)()()( max)(
Banks: liquidity risks
LiIdsiIdiMiFFiL od
MrdeYeY-- r
e
e
-
)()()( max)(
)(1 eY- siio
e--d-d-rd )ˆ)(1( LLLM Ls
isiLLL
o
d
-Y-d-d-rd -1)ˆ)(1(
LI de-e )(
e
r eYed-rd---d-d- )()()ˆ)(1()()( dLsLiiLLiiL odo
FOC
Banks: liquidity risks
Ls
isiLLLM
o
d
-Y-d-d-rd -1)ˆ)(1(
LI de-e )(
e
r eYed-rd---d-d- )()()ˆ)(1()()( dLsLiiLLiiL odo
Banks: liquidity risks
General result on the role of reserve requirements
• risk averse investors
• lack of bank segmentation
• dynamics
Interbank market clearing → i
Nominal side (solvency risk) based on Bernanke, Gertler and Gilchrist (1999) for the relation betweenbanks and depositors (DI)
- Friction 2: realization of x is private information of banks (investors)
- CSV setup between banks and depositors(standard debt contract)
Banks: solvency risks
t = 0 A LBank
Loan entrep.
Assets dQ Equity dQ
dL
dQ
dL
M
Loan from CB M
FF
dL + FFDeposit worker
I
Reserves M + FF – I
Loan interb. I
Net worth
x(1 + il)dL + dQ + (L) – (1 + id)dL
Banks: solvency risks
t = 0
dQ
dL
M
FF
I
Net worth (solvent bank)
x(1 + il)dL + dQ + (L) – (1 + id)dL ≥ 0
Banks: solvency risks
xLi
LQLix
l
d
d
-d-d
)1(
)()1(
xx xx
monitoring
cost f(1 + il)dL
depositors take everything
no monitoring
(1 + id)dL
(insolvent) (solvent)
Given il, dQ, and the risk-free rate, if, the problem of thebank is to choose loans dL (leverage), and thresholdrepayment ratio x to maximize equity premium
subject to participation of depositors (DI)
Qi
xdLiLQLix
f
x
dl
d
Xd-dd
)1(
)()1()()1(
1
LixdLQLixxLi f
x
ld dXddf-X-d )1()()()1()1()(1)1(0
and capital constraint
Q ≥ k L
Banks: solvency risks
subject to
Qi
xdLiLQLix
f
x
dl
xL d
Xd-dd
)1(
)()1()()1(
max
1
,
LixdLQLixxLi f
x
ld dXddf-X-d )1()()()1()1()(1)1(0
→ L, x
Q ≥ k L
Banks: solvency risks
Determine s from
)(1)1(1 xsii X-
Determine il from arbitrage condition
1
)1(
)()()1()1(
1
d
Xd-dd
Qi
xdLLiQLix
f
x
dl
Banks: solvency risks
As long as reserve requirements (r) do not affect (L), they do not have an effect either in bank intermediation
siiiIMxL dl , , , , , , ,
Determine id from
xLi
LQLil
d
d
-d-d
)1(
)()1(
• Parameters: d, f; io, ir, if; r, k; X(x), Y(e)
Calibration
→ size of banks: d
→ monitoring costs: f
→ policy rates: io, ir, if
→ regulation: r, k
Data (FDIC): average share of loans and leasesd = 0.0001
Data (FDIC): average losses from bankruptcy over depositsf = 0.22
Data (Fed.): average refinancing rate average 3-month T-bill rate
Data (BIS): capital requirement Basel I & II
ir = 0
io = 0.0278
if = 0.0257
k = 0.08r = 0
Calibration
→ distribution of performing loans: X(x)Match: mean and standard deviation of NPL ratio
• Parameters: d, f; io, ir, if; r, k; X(x), Y(e)
Lognormal(mx = 5.8606; sx = 0.3595) truncated at x = 1
0
0.2
0.4
0.6
0.8
1
0.5 0.6 0.7 0.8 0.9 1
x
X(x) and empirical distribution of performing loans
Calibration
→ distribution of performing loans: X(x)
→ distribution of liquidity shocks Y(x)
Match: interbank trade over loans
Lognormal(mx = 5.8606; sx = 0.3595) truncated at x = 1
Normal(me = 0; se = 0.2131)
• Parameters: d, f; io, ir, if; r, k; X(x), Y(e)
KS test at 10% wrt empirical distribution of NPL
Match: mean and standard deviation of NPL ratio
8.5
8.6
8.7
8.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
r
BANK LEVERAGE (ir = 0)
0
0.02
0.04
0.06
0.08
0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r
Lending rate and deposit rate (ir = 0)
• Nominal model with…
Conclusions
• …endogenous bank leverage (solvency risk)
• …demand for reserves (liquidity risk)
• …instruments of MP (official rates, reserve req.)
• …interbank market
• …bank regulation (capital requirements)
• In the model…
Conclusions
• …flexible prices
• …only important frictions
• …MP has real effects in the short run (changes in io)
• segmentation in bank loan market
• information frictions
Conclusions
• Effects of reserve requirements
Realized net worth after realization of x
)()1()1( LLiQLix dl d-dd
e
r eYed-rd---d-d- )()()ˆ)(1()()( dLsLiiLLiiL odo
• if io = ir no effect on equilibrium no matter what r is
• for 0 ≤ r < 1 DI needed to prevent bank run equilibrium
A LBank
Loan entrep.
Assets dQ Equity dQ
dL
Loan from CB M
dL + FFDeposit worker
Reserves M + FF – I
Loan interb. I
• Role of collateral
• M < dQ may not be enough to support narrow banking
Ls
isiLLLM
o
d
-Y-d-d-rd -1)ˆ)(1(
• M < dQ + dL (securitization)?
Conclusions
• Role of collateral
Conclusions
• Seigniorage
A LCentral Bank
OMOs
Assets
Required
Reserves
Currency
Excess
• The model could incorporate…
Conclusions
• …heterogeneous banks
• size (money market dichotomy)
• …unconventional MP (QE)
• …DSGE + endogenous risk cycles
• risk profiles (solvency and liquidity)
• …
• Banks as creators of money
Literature review
Goodfriend & McCallum (JME, 2007)
Bianchi & Bigio (NBER, 2014)
Chari & Phelps (JME, 2014)
Jakab & Kumhof (BofE, 2015)
Disyatat (JMCB, 2011)
Benes & Kumhof (IMF, 2012)
Thanks for your attention